Heat kernel of non-minimal second-order operators

TL;DR

This paper derives a model-independent expression for the heat kernel coefficient of non-minimal second-order operators and demonstrates its application through examples, including a toy-model of dynamical torsion.

Contribution

It provides the first model-independent derivation of the local trace of the heat kernel coefficient for non-minimal second-order operators.

Findings

Derived the local part of the heat kernel coefficient in a model-independent way

Applied the results to practical examples including dynamical torsion

Confirmed compatibility with existing literature

Abstract

We analyze the spectra of general non-minimal second-order operators. To do this, we derive the local part of the trace of the second Seeley-DeWitt heat kernel coefficient for such operators in a completely model-independent way. Afterwards, we provide three examples to show how our result can be applied in practical scenarios. In particular, we emphasize this discussion when dealing with a toy-model of dynamical torsion, which is viewed as a simple instance of higher-spin fields. All our results are compatible with the literature, and we provide a Mathematica notebook with the model-independent results that are written in the paper.